Question

a vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. how much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup​

Answer 1

Suppose the vessel initially contains 8 liters of liquid.

Let x liters of this liquid be replaced with water.

Water in new mixture = (3-3x/8+x)

Syrup in new mixture = (5-5x/8)

Then (3-3x/8+x) = (5-5x/8)

5x + 24 = 40 - 5x

10x=16

==>x=8/5

So part of mixture replaced is 8/5*1/8=1/5